Andrew Boothroyd

Abstract:

Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in the field. I begin by outlining the relevant concepts from topology, then give a summary of the theory of non-interacting electrons in periodic potentials. Next, I explain the concepts of the Berry phase and Berry curvature, and derive key formulae. The remainder of the article deals with how these ideas are applied to classify crystalline solids according to the topology of the electronic states, and the implications for observable properties. Among the topics covered are the role of symmetry in determining band degeneracies in momentum space, the Chern number and 𝒵2 topological invariants, surface electronic states, two- and three-dimensional topological insulators, and Weyl and Dirac semimetals

Abstract:

Inelastic neutron scattering is used to study the magnetic excitations of the S=1 square-lattice antiferromagnet La₂NiO₄. We find that the spin waves cannot be described by a simple classical (harmonic) Heisenberg model with only nearest-neighbor interactions. The spin-wave dispersion measured along the antiferromagnetic Brillouin-zone boundary shows a minimum energy at the (1/2,0) position as is observed in some S=1/2 square-lattice antiferromagnets. Thus, our results suggest that the quantum dispersion renormalization effects or longer-range exchange interactions observed in cuprates and other S =1/2 square-lattice antiferromagnets are also present in La₂NiO₄. We also find that the overall intensity of the spin-wave excitations is suppressed relative to linear spin-wave theory, indicating that covalency is important. Two-magnon scattering is also observed.